Metaheuristic Algorithm Approach to Solve Non-Linear Equations System with Complex Roots

Abstract

Non-linear equations system is a collection of some non-linear equations that will find the best solution. Finding the solution of non-linear equations system usually by using analytical method, but there are some complex cases that cannot be solved analytically, so new methods are needed to solve them. One method that can be used to solve non-linear equations system is by using metaheuristic algorithm. This research aims to solve non-linear equations system with complex roots by using metaheuristic algorithm. The metaheuristic algorithm used in this research is Particle Swarm Optimization (PSO), Firefly Algorithm (FA) and Cuckoo Search (CS). The input of this research is non-linear equations system that will be tested and parameters of the PSO, FA, and CS algorithm. Non-linear equations system which is the object of problem is polynomial function and transcendent function, which include logarithmic function, first degree trigonometric function and exponential function. The resulting output is an approximation of the complex roots and function value. Then the obtained solution of non-linear equations system compared with the result of accuracy by finding the value of the function f(x) which is closer to zero. The result of this research obtained by comparing the value of the function produced by each algorithm showed that Particle Swarm Optimization (PSO) algorithm is better at solving non-linear equations system with complex roots because the value of the resulting function is close to zero.